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You make a new sequence by removing 2 elements from the sequence {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}. What is the standard deviation of the new sequence?

(1) The median of the new sequence is 10.(2) The new sequence has the same average as the original sequence.

Pick E in this one.
(1) in order to maintain the median of 10, we have several cases:
Keep (9,11) , we can remove any number of the rest : one number in the left side of (9,11) and another in the right side of (9,11).
For example: remove 1 and 19 ...then compare with removal of (3,19). The two standard deviations are different ---> that means we can't have exactly the same SD for all removals ---> can't find such SD --> insuff

(2) this statement means: the two removed numbers have a sum which is equal to mean*2 . The mean here is 10 . Thus, the pairs of removal can be either ( 1,19) , (3,17) , (5,15) , (3,13) , (9,11) . Since the mean is unchanged, the removal of (1,19) yields a smaller SD than that of (3,13) because (1,19) has wider distances to the mean than (3,13) does. --> no common SD for all removal --> insuff